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Analysis of a Finite State Many Player Game Using Its Master Equation

27 Pages Posted: 18 Jul 2017  

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Asaf Cohen

University of Michigan at Ann Arbor - Department of Mathematics

Date Written: July 9, 2017

Abstract

We consider an n-player symmetric stochastic game with weak interaction between the players. Time is continuous and the horizon and the number of states are finite. We show that the value function of each of the players can be approximated by the solution of a partial differential equation called the master equation. Moreover, we analyze the fluctuations of the empirical measure of the states of the players in the game and show that it is governed by a solution to a stochastic differential equation. Finally, we prove the regularity of the master equation, which is required for the above results.

Keywords: Game theory, Mean-field games, master equation, fluctuations, finite state control problem, Markov chains

Suggested Citation

Bayraktar, Erhan and Cohen, Asaf, Analysis of a Finite State Many Player Game Using Its Master Equation (July 9, 2017). Available at SSRN: https://ssrn.com/abstract=3001348

Erhan Bayraktar (Contact Author)

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Asaf Cohen

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

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